
Gass / / Vs ^NJ 
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{From the American Naturalist, October, i88l.) 

AN ATTEMPT TO RECONCILE THE DIFFERENCES 
BETWEEN AUTHORITIES IN REFERENCE TO 
THE MAYA CALENDAR AND CERTAIN 
DATES; ALSO TO DETERMINE 
THE AGE OF THE MANU- 
SCRIPT TROANO. __ 

BY PROFESSOR CYRUS THOMAS, 1883 

IN my former paper (American Naturalist for August, ,i,^SjA^^^. 
I reached the following conclusions : ^.c^ — .^■^-"^ 

First. — That the Ahau or Katun consisted of twenty-four 
years. 

Second. — That but twenty of these years were usually counted. 

Third. — That the grand cycle consisted of 312 years. 

Fourth. — That the cycles began with the year i Cauac, or in 
other words that the Cauac column in the table of years should 
stand at the left. 

Two important points yet remain to be determined before we 
are in a condition to compare Maya dates with those of the 
Christian era : 

First. — The position of the different Katunes according to their 
numbers in the grand cycle. 

Second. — Some one year of the Christian era that corresponds 
with some one year of a given Katun, or, in other words, to 
determine one or more contemporaneous dates of the two 
systems. 

Before entering upon the discussion of the topic mentioned in 
the title to this paper, I wish to present the following additional 
proof that the year series commenced with a Cauac year, as this 
is a point which must be settled before we can feel certain in 
regard to any comparison made between dates of the two 
systems. 

In the manuscript discovered by Perez and translated into 
English by Stephens, we find the following statement : 

" In the 13th Ahau, Chief Ajpula died. Six years were want- 
ing to complete the 13th Ahau. This year was counted towards 
the east of the wheel and began on the 4th Kan. Ajpula died 
on the 1 8th day of the month Zip, on 9 Ymix; and that it may 
be known in numbers, it was the year 1536, sixty years after the 
demolition of the fortress." 

As the years could only begin with one of the four days, 

/<p<f// 



768 The Maya Calendar and the Age of MS. Troano. [October, 

Cauac, Kan, Muluc, lie, which followed each other in the order 
here given, it is evident this Ahau must have ended on 10 Ix, and 
must have commenced with 13 Cauac, if we count 24 years to 
the Ahau. As I have shown in the previous paper that this 
period consisted of 24 years, I shall assume that point as settled, 
and will give, opposite, a table of years sufficiently extended to 
cover one entire grand cycle, also the closing cycle of the prece- 
ding, and the first of the following grand cycles, showing the 
position of the Ahaues. 

As the grand cycle includes just 13 Katunes — 312 years — I 
take for granted that the first year of this period coincides with 
the first year of a Katun, and consequently the close of the for- 
mer coincides with the close of a Katun. By dividing the for- 
mer into periods of twenty-four years, we will obtain the positions 
of the Katunes, and our next step will be to find their respective 
numbers. 

The commencement and ending of the great cycle are marked 

thus • — ■ xi^""" — ; the divisions between the Ahaues with single 

transverse solid black lines. According to the quotation just 
made from the Perez manuscript, the 13th Ahau was one that 
required six years to complete it after the year 4 Kan. This can 
only be found in the one I have numbered xiii (the Roman 
numerals indicate the numbers of the Ahaues or Katunes). If 
we take for granted that theperiods were numbered thus, 13, 11, 
9> 7> 5> 3> i> 12, 10, 8, 6, 4, 2 — a point in reference to which all the 
authorities agree — having determined the number of one in the 
grand cycle, it is an easy matter to number the rest. 

I call special attention to the fact that the one numbered^xiii, 
found as above stated, begins with the year 13 Cauac; also that 
the first years of the others correspond with numbers and order 
as given in the above series. The selection of xiii as the one 
with which to begin the series, was, as Dr. Valentini has given 
good reasons for believing, an arbitrary proceeding on the part of 
the Maya priests. 

This numbering, as any one can see, agrees precisely with the 
position and numbers of the periods marked in table xi of my 
previous article (p. 639). The position and numbers of these 
periods, as I have given them here (Table xii) agree exactly with 
the dates in the Manuscript Troano and the Perez manuscript. 

As 4 Kan of the 13th Ahau coincides with the year 1536 of 

















TABLE 


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1518 
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1 88 1.] The Maya Calendar and the Age of MS. Tvoano. 769 

the Christian era, we can from this easily change the years of one 
system into those of the other. For convenience, I have marked 
on the table the year of our era corresponding with the first and 
last of each Ahau.^ 

Now let us test this arrangement by the two or three additional 
dates found on record, and which the authorities have failed to 
make agree with any explanation of the calendar heretofore 
given. 

Bishop Landa (" Relacion de Cosas," § 41) states that, "The 
Indians say, for example, that the Spaniards arrived in the City 
of Merida the year of the nativity of our Lord and Master 1541, 
which was precisely the first year of 1 1 Ahau." 

As the Indians could have given dates only by their system 
and by the number of years, it follows that the Bishop connected 
the year 1541 of the one system with that of the first of the nth 
Ahau by his own calculation. 

As he understood the twenty usually counted years to form a 
complete Ahau, and supposed one of these to follow another 
without any intervening years, he would take 9 Muluc of the 13th 
Ahau — which was 1541 according to my table — as the first of 
the nth Ahau (13 Muluc), according to his understanding. 

In order to make this plain I have surrounded the usually 
counted years of the 13th and nth Ahaues with light waved 
lines. I have marked the two years he has confounded (9 and 
13) with a star; the year 4 Kan of the 13th Ahau, which cor- 
responds with our year 1536, is surrounded by a dark circle. 

We know from his express statement that he understood 
twenty years to constitute one of these periods, a fact which will 
probably explain the discrepancy in relation to another date which 
he mentions. 

While writing his work in 1566, he remarks, "According to 
the computation of the Indians, it is now 1 20 years since Maya- 
pan was abandoned." As this period must have been understood 
by him to include six Ahaues, the number as corrected would 
be 144 years, substituting this number and counting back we 
obtain the year 1422 or 1423 — the last year of the loth Ahau, or 
first of the 8th, as the one in which the destruction occurred. 

Cogulludo (as stated by Dr. Valentini) places this event " about 

^No notice is taken here of the fractional differences between the years of the two 
systems. 



770 The Maya Calendar and the Age of MS. Troano. [October, 

the year 1420 A. D." The Perez manuscript locates it in the 8th ^ 
Ahau — the one following the loth — but without giving the year. 
As my calculation places it in the last year of the loth, or first of 
the 8th, the agreement is perhaps as close as could be expected. 

Perez states that the year 1392 of our era was the Maya year 
7 Cauac, " according to all sources of information, confirmed by 
the testimony of Don Cosme de Burgos, one of the conquerors 
and a writer (but whose observations have been lost." — (Bancroft, 
II, 763). The correctness of this statement has been very seri- 
ously questioned because of the apparent impossibility of making 
it agree with the other dates. In the first place Perez started 
wrong by taking for granted that 7 Cauac was the first year of an 
Ahau, a supposition by no means necessary. In the second place 
it is more than probable he arrived at the date 1392 by calcula- 
tion from the data he had before him, and not from the fact that 
the two dates were connected by the authority quoted from. It 
is certain that he or his authority must have reduced the years of 
one system to those of the other to have arrived at this date. 

As he gives, in his calculations, the year 1493 as that on which 
Ajpula died, instead of 1536, as stated by his manuscript, thus 
antedating it by forty-three years, it is probable that this error 
runs through all his calculated dates. Now let us make this cor- 
rection on our table by counting from the year 1392, as found 
there, and see what year it brings us to. 

Examining the table, we see that the 12th Ahau closed with 
1398, and that 1392, according to my arrangement, was the year 
3 Kan of this Ahau. Counting from this forward through the 
six remaining years of this Ahau, the 24 of the loth to the 13th 
year of the 8th Ahau (43 in all), we reach 7 Cauac ; precisely the 
date required by his authorities. It also falls in the 8th Ahau, a 
fact which also appears to be demanded by his data; but it is the 
year 1435 of our era and not 1392. Is it not more than probable 
that this was the year in which Mayalpan was destroyed ? It is 
a little strange that Perez should have made the mistake of say- 
ing that Ahau No. 2, in which his manuscript places the first 
appearance of the Spaniards on the coast of Yucatan, ended with 
the year 1488, and that Dr. Valentini should have overlooked this 
error. According to my scheme, this Ahau began with 1495 and 
ended with 15 18, covering the correct date. 

Brasseur (Relac. cles cos. 52 note) says erroneously, " 6th." 



1 88 1.] The Maya Calendar and the Age of MS. Troano. yyi 

We see from this that when the Maya calendar is properly ex- 
plained, and the manifest errors of the various authorities cor- 
rected, the dates can be reconciled, and in fact furnish strong 
evidence of the correctness of what I have advanced in reference 
to the proper position and numbers of the Ahaues in the grand 
cycle. 

The theory advanced by Perez that the Ahaues were numbered 
from the second day of the Cauac years, is simply a supposition 
based upon the name " Ahau," and the fact that the numbers of 
these periods, as usually given, can be found in this way. and is 
really the basis of all his calculations. 

But we can find the same numbers, and in the order given, 
without resorting to this theory, as will be seen by reference to 
the table. Dividing the series into periods of 24 years will neces- 
sarily give these numbers as the first years, no matter where we 
commence the division. As will be seen by reference to the 
table, the Ahau in which the year 1536 falls, and which the 
Perez manuscript states was the 13th, commences with the year 
1 3 Cauac, the next with 1 1 Cauac, and so on, precisely as given 
by all authorities. The onlv foundation, therefore, for the theory 
advanced by Perez, was the aame " Ahau," which was doubtless 
applied to these periods on account of their importance in calcu- 
lations of time and in giving dates. 

Is there anything in the manuscript itself indicating the date 
at which it, or the original from which the one discovered was 
copied, was written ? 

The period embraced by the four plates xx-xxiii, which can be 
located in the series of years with reasonable if not absolute cer- 
tainty, is evidently peculiar and not a part of the Maya calendar 
system. If, as I have given strong reasons for believing, it marks 
the close of one great cycle and the commencement of another, it 
will be located as shown by the heavy waved line on the table. 

Why was this peculiar period given ? My answer is that it 
probably marks the time during which the author lived, and 
hence was written during the latter half of the fourteenth 
century. 

That exactly the same combinations may be found by going 
back one grand cycle, or 312 years, is true, but the internal as 
well as the external evidence, which I cannot undertake to discuss 
here, will not, in my opinion, allow us to carry it back to such a 



7/2 The Maya Calendar and the Age of MS. Troano. [October, 

remote period as the commencement of the eleventh century ; 
that we cannot bring it down to the middle of the seventeenth 
century (the only possible subsequent date on the above supposi- 
tion) must be admitted. 

That the peculiar period embraced in plates xx-xxiii may be 
located where any two cycles meet is certainly true, so far as the 
years are concerned, but judging by the symbols and extent of 
the period, certain signs which seem to indicate the 3d and ist 
Ahau, and from the fact that the commencement of no other 
cycle, except that with which the grand cycle begins, coincides 
with the commencement of an Ahau, I am satisfied it marks the 
union of two of the greatest Maya periods.^ 

^Errata in the First Article. — In second line from the bottom of page 631, after 
the words "I7tli day of the 2d" add "or 15th," so as to read " 17th day of the 
2d or 15th month." In third line from the top of page 636, for " governing" read 
"covering." In second line from the top of page 639, for "each period" read 
" each two periods." 



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